MCQOPTIONS
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MCQOPTIONS
This section includes 108 Mcqs, each offering curated multiple-choice questions to sharpen your Mathematics knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
The product of the polynomials, \[(3{{u}^{2}}v-5u{{v}^{2}})\] and \[\left( \frac{1}{5}{{u}^{2}}+\frac{1}{5}{{v}^{2}} \right)\] is |
| A. | \[\frac{3}{5}{{u}^{4}}v-{{u}^{3}}{{v}^{2}}-u{{v}^{4}}+\frac{3}{5}{{u}^{2}}{{v}^{3}}\] |
| B. | \[\frac{{{u}^{4}}v}{5}-2u{{v}^{2}}\,+{{u}^{2}}{{v}^{3}}\,-\frac{5u{{v}^{4}}}{3}\] |
| C. | \[\frac{3{{u}^{4}}v}{5}-4{{v}^{2}}+4{{u}^{2}}{{v}^{3}}-\frac{5u{{v}^{4}}}{3}\] |
| D. | \[\frac{3{{u}^{4}}v}{5}-{{u}^{3}}{{v}^{2}}+{{u}^{2}}{{v}^{3}}-5u{{v}^{4}}\] |
| Answer» B. \[\frac{{{u}^{4}}v}{5}-2u{{v}^{2}}\,+{{u}^{2}}{{v}^{3}}\,-\frac{5u{{v}^{4}}}{3}\] | |
| 2. |
If \[a+b+c=0\], the value of \[\frac{{{a}^{2}}}{bc}+\frac{{{b}^{2}}}{ca}+\frac{{{c}^{2}}}{ab}\]is |
| A. | 1 |
| B. | 0 |
| C. | -1 |
| D. | 3 |
| Answer» E. | |
| 3. |
The expansion of log \[{{\log }_{e}}\frac{1}{(1-x)}\]is |
| A. | \[x-\frac{{{x}^{2}}}{2}+\frac{{{x}^{3}}}{3}-\,.....\] |
| B. | \[x+\frac{{{x}^{2}}}{2}+\frac{{{x}^{3}}}{3}+\,.....\] |
| C. | \[1-x+\frac{{{x}^{2}}}{2}-\frac{{{x}^{3}}}{3}+\,.....\] |
| D. | \[1+x-\frac{{{x}^{2}}}{2}+\frac{{{x}^{3}}}{3}-\,.....\] |
| Answer» C. \[1-x+\frac{{{x}^{2}}}{2}-\frac{{{x}^{3}}}{3}+\,.....\] | |
| 4. |
Read the following statements carefully and choose the correct answer. (i) I had Rs. 200 with me. I gave Rs. x to Anwar, Rs. \[\frac{x}{2}\] to Vidhu and I am left with Rs. \[\frac{x}{2}\]. The algebraic form of the given statement is written as: \[x+\frac{x}{2}+\frac{x}{2}=200\] (ii) The amount I gave to Vidhu is Rs 50 and to Anwar is Rs 100. |
| A. | Only (i) is true. |
| B. | Only (ii) is true. |
| C. | Both (i) and (ii) are false. |
| D. | (ii) is a solution of (i). |
| Answer» E. | |
| 5. |
For which of the following function is : \[\frac{f-f}{a-b}\] Constant for all number a and b where \[a\ne b\]? |
| A. | \[f(x)=4x+7\] |
| B. | \[f(x)=x+{{x}^{2}}\] |
| C. | \[f(x)=\cos x\] |
| D. | \[f(x)={{\log }_{e}}x\] |
| Answer» B. \[f(x)=x+{{x}^{2}}\] | |
| 6. |
DIRECTIONS: The questions in this segment consists of two statements, one labelled as ?Assertion A? and the other labelled as ?Reason R?. You are to examine these two statements carefully and decide if the Assertion A and Reason R are individually true and if so, whether the reason is a correct explanation of the assertion. Select your answers to these items using codes given below. Assertion (A): Value of \[{{\left( \frac{4}{9} \right)}^{\frac{3}{2}}}\times {{\left( \frac{4}{9} \right)}^{\frac{1}{2}}}\]is \[{{\left( \frac{4}{9} \right)}^{2}}.\] Reason (R): For any two rational numbers a and b and for any integers m and n, we have \[{{a}^{m}}\times {{a}^{n}}={{a}^{m+n}}\] |
| A. | If both Assertion and Reason are correct and Reason is the correct explanation of Assertion. |
| B. | If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion. |
| C. | If Assertion is correct but Reason is incorrect. |
| D. | If Assertion is incorrect but Reason is correct. |
| Answer» B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion. | |
| 7. |
If \[x-\frac{1}{x-2}=2-1\frac{1}{x-2}\] , then x is equal to |
| A. | 1 |
| B. | 2 |
| C. | 1 |
| D. | None of these |
| Answer» E. | |
| 8. |
What is the value of "n" that makes the equation below true? \[\frac{n}{3}=12\]. |
| A. | 36 |
| B. | 12 |
| C. | 9 |
| D. | 3 |
| Answer» B. 12 | |
| 9. |
The equation \[\frac{(x+2)(x-5)}{(x-3)(x+6)}=\frac{x-2}{x+4}\] has |
| A. | 3 roots |
| B. | 2 roots |
| C. | 1 root |
| D. | no root |
| Answer» D. no root | |
| 10. |
If \[x+\frac{1}{x}=5\] (where\[x\ne 0\]) then find \[\frac{2x}{3{{x}^{2}}-5x+3}=?\] |
| A. | \[\frac{1}{2}\] |
| B. | \[\frac{1}{3}\] |
| C. | \[\frac{1}{4}\] |
| D. | \[\frac{1}{5}\] |
| Answer» E. | |
| 11. |
If \[x=y=z\] then find \[\frac{{{\left( x+y+z \right)}^{2}}}{{{x}^{2}}+{{y}^{2}}+{{z}^{2}}}\] |
| A. | 9 |
| B. | 3 |
| C. | 4 |
| D. | 1 |
| Answer» C. 4 | |
| 12. |
If \[a+\frac{4}{a}=4\] (Here\[a\ne 0\]) then find\[{{a}^{2}}+\frac{1}{{{a}^{3}}}=\]? |
| A. | \[2\frac{1}{8}\] |
| B. | \[3\frac{1}{8}\] |
| C. | \[4\frac{1}{8}\] |
| D. | \[5\frac{1}{8}\] |
| Answer» D. \[5\frac{1}{8}\] | |
| 13. |
Evaluate: \[{{\left( \frac{2}{7} \right)}^{\frac{1}{2}}}\times {{\left( \frac{2}{7} \right)}^{\frac{3}{2}}}\] |
| A. | \[{{\left( \frac{2}{7} \right)}^{\frac{3}{4}}}\] |
| B. | \[{{\left( \frac{2}{7} \right)}^{-1}}\] |
| C. | \[\frac{4}{49}\] |
| D. | \[\frac{49}{4}\] |
| Answer» D. \[\frac{49}{4}\] | |
| 14. |
If \[x-\frac{1}{x}=9,\] find the value of\[a{{x}^{2}}+\frac{1}{{{x}^{2}}}=\]? |
| A. | 83 |
| B. | 84 |
| C. | 85 |
| D. | 86 |
| Answer» B. 84 | |
| 15. |
If \[\frac{\sqrt{3}-1}{\sqrt{3}+1}=a+b\sqrt{3}\], then the value of 'a' and 'b' is |
| A. | \[\text{a }=\text{2},\text{ b}=-\text{ 1}\] |
| B. | \[\text{a }=\text{2},\text{ b}=-\text{ 1}\] |
| C. | \[\text{a }=\text{ }-\text{ 2},\text{ b }=\text{ 1}\] |
| D. | \[~\text{a }=\text{ }-\text{ 2},\text{ b }=\text{ }-\text{ 1}\] |
| Answer» B. \[\text{a }=\text{2},\text{ b}=-\text{ 1}\] | |
| 16. |
Solve:\[\frac{3}{4}\left( 7x-1 \right)-\left( 2x-\frac{1-x}{2} \right)\] \[=x+\frac{3}{2}\] then \[x=?\] |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» B. 2 | |
| 17. |
If \[\left( x+\frac{1}{x} \right)=\frac{10}{3},\] then \[{{\left( x-\frac{1}{x} \right)}^{2}}\] is |
| A. | \[{{\left( \frac{7}{3} \right)}^{2}}\] |
| B. | \[{{\left( \frac{8}{3} \right)}^{2}}\] |
| C. | \[{{\left( \frac{10}{3} \right)}^{2}}\] |
| D. | \[{{\left( \frac{5}{3} \right)}^{2}}\] |
| Answer» C. \[{{\left( \frac{10}{3} \right)}^{2}}\] | |
| 18. |
The sum of a number and its reciprocal is \[\frac{125}{22}\]The number is |
| A. | \[\frac{2}{11}\] |
| B. | \[\frac{1}{11}\] |
| C. | \[\frac{3}{11}\] |
| D. | None of these |
| Answer» B. \[\frac{1}{11}\] | |
| 19. |
The value .of \[{{\left( \frac{{{x}^{b}}}{{{x}^{c}}} \right)}^{\frac{1}{bc}}}.{{\left( \frac{{{x}^{c}}}{{{x}^{a}}} \right)}^{\frac{1}{ca}}}.{{\left( \frac{{{x}^{a}}}{{{x}^{b}}} \right)}^{\frac{1}{ab}}}\] on simplifying is |
| A. | \[x\] |
| B. | \[\frac{1}{x}\] |
| C. | 1 |
| D. | -1 |
| Answer» D. -1 | |
| 20. |
What is the total number of candidates appear in an examination, if 31% is fail and the number of passed candidates are 247 more than the number of fail candidates? |
| A. | 650 |
| B. | 750 |
| C. | 800 |
| D. | 900 |
| E. | None of these |
| Answer» B. 750 | |
| 21. |
If the duty on an article be reduced by 40% of its present amount, then by how much percent must the consumption be increased in order that the revenue may remain unaltered? |
| A. | 0.5 |
| B. | \[166\frac{2}{3}\,\,%\] |
| C. | 0.4 |
| D. | 0.2 |
| E. | None of these |
| Answer» C. 0.4 | |
| 22. |
Stephen's mathematics test had 85 problems, which contains 20 algebra, 30 statistics and 35 geometry problems. He answered 70% of algebra, 40% of the statistics and 60% of geometry problems correctly. He did not pass the test because he got less than 60% of the problem correct. How many more questions he would have needed to answer correctly to earn 60% passing grade? |
| A. | 5 |
| B. | 4 |
| C. | 1 |
| D. | 3 |
| E. | None of these |
| Answer» C. 1 | |
| 23. |
In a certain year the population of London is 200000. If it increases at the rate of 6.5 % per annum then what will be its population after 2 years? |
| A. | 226845 |
| B. | 228645 |
| C. | 224685 |
| D. | 228465 |
| E. | None of these |
| Answer» B. 228645 | |
| 24. |
The ratio of ages of Marry and Mariya is 4 : 5. After 12 years their ratio becomes 5 : 6. What will be the age of Marry after 2 years? |
| A. | 49 |
| B. | 50 |
| C. | 60 |
| D. | 70 |
| E. | None of these |
| Answer» C. 60 | |
| 25. |
In a container, water and milk are mixed in the ratio 5 : 3. If 16 litres of mixture are removed and same quantity of milk be added then the ratio becomes 3 : 5. What is the volume of the container? |
| A. | 40 |
| B. | 50 |
| C. | 60 |
| D. | 70 |
| E. | None of these |
| Answer» B. 50 | |
| 26. |
Find the product of \[\left( \mathbf{2x}+\mathbf{4y} \right)\left( \mathbf{3x}-\mathbf{2y} \right),\] |
| A. | \[6{{x}^{2}}+8xy-8{{y}^{2}}\] |
| B. | \[{{x}^{2}}-8xy-8{{y}^{2}}\] |
| C. | \[8{{x}^{2}}-xy-8{{y}^{2}}\] |
| D. | All of these |
| E. | None of these |
| Answer» B. \[{{x}^{2}}-8xy-8{{y}^{2}}\] | |
| 27. |
Subtract the following: \[{{\mathbf{x}}^{\mathbf{3}}}-\mathbf{3}{{\mathbf{x}}^{\mathbf{2}}}-\mathbf{5x}+\mathbf{4}\]from \[\mathbf{3}{{\mathbf{x}}^{\mathbf{3}}}-{{\mathbf{x}}^{\mathbf{2}}}+\mathbf{2x}-\mathbf{4}.\] |
| A. | \[2{{x}^{3}}+2{{x}^{2}}+7x-8\] |
| B. | \[-2{{x}^{5}}-7x+8\] |
| C. | \[2{{x}^{3}}-2{{x}^{2}}-4x-8\] |
| D. | All of these |
| E. | None of these |
| Answer» B. \[-2{{x}^{5}}-7x+8\] | |
| 28. |
If \[\mathbf{4}{{\mathbf{x}}^{\mathbf{84}}}\mathbf{-7}{{\mathbf{x}}^{\mathbf{42}}}\mathbf{-4}{{\mathbf{x}}^{\mathbf{70}}}\mathbf{-7}{{\mathbf{x}}^{\mathbf{35}}}\mathbf{=200}\] is divided by \[{{\mathbf{x}}^{\mathbf{14}}}\mathbf{-14}\]. Which one of the following is the first term of the question? |
| A. | \[-4{{x}^{70}}\] |
| B. | \[-4{{x}^{60}}\] |
| C. | \[4{{x}^{70}}\] |
| D. | All of these |
| E. | None of these |
| Answer» D. All of these | |
| 29. |
Find the value of x in the equation\[\mathbf{2}\left( \mathbf{5x}+\mathbf{3} \right)\mathbf{1}=\mathbf{65}\]. |
| A. | 11 |
| B. | 6 |
| C. | 3 |
| D. | 5 |
| E. | None of these |
| Answer» C. 3 | |
| 30. |
If 7 times of a number is 98, then the number is: |
| A. | 28 |
| B. | 21 |
| C. | 7 |
| D. | 14 |
| E. | None of these |
| Answer» E. None of these | |
| 31. |
In the expression \[{{\mathbf{a}}^{\mathbf{2}}}+\mathbf{3a}\mathbf{1}\], the coefficient of \[{{\mathbf{a}}^{\mathbf{2}}}\] is: |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | 3 |
| E. | None of these |
| Answer» C. 2 | |
| 32. |
The value of = 21 and the value of =24, so the value of will be: |
| A. | 14 |
| B. | 12 |
| C. | 13 |
| D. | 15 |
| E. | None of these |
| Answer» D. 15 | |
| 33. |
If the total weight of the apples shown below is 984 grams, then the weight of 5 such apples will be: |
| A. | 720 grams |
| B. | 615 grams |
| C. | 725 grams |
| D. | 675 grams |
| E. | None of these |
| Answer» C. 725 grams | |
| 34. |
A packet of 1 kg sugar costs Rs. 52. What will be the cost of 4 such packets? |
| A. | Rs. 204 |
| B. | Rs. 208 |
| C. | Rs. 156 |
| D. | Rs. 210 |
| E. | None of these |
| Answer» C. Rs. 156 | |
| 35. |
Find the value of x, if\[{{\mathbf{(}\sqrt{\mathbf{6}}\mathbf{)}}^{\mathbf{x-2}}}\mathbf{=1}\]. |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| E. | None of these |
| Answer» C. 3 | |
| 36. |
If 945 balls can be put in 7 boxes, then how many balls can be put in 9 such boxes? |
| A. | 1045 |
| B. | 1215 |
| C. | 1165 |
| D. | 1385 |
| E. | None of these |
| Answer» C. 1165 | |
| 37. |
If 10 pears cost Rs.72, then how many pears can you buy if you have Rs. 36? |
| A. | 3 |
| B. | 4 |
| C. | 5 |
| D. | 6 |
| E. | None of these |
| Answer» D. 6 | |
| 38. |
The factor of 4p2 + q2 + 16 - 4pq + 8q - 16p is: |
| A. | (-2p - q + 4) (-2p + q + 4) |
| B. | (2p + q + 4) (2p +q + 4) |
| C. | (-2p + q + 4) (-2p + q + 4) |
| D. | (-2p + q - 4) (-2p + q - 4) |
| E. | None of these |
| Answer» D. (-2p + q - 4) (-2p + q - 4) | |
| 39. |
Find the cube of x - 2y. |
| A. | \[{{\operatorname{x}}^{3}}+ 8{{y}^{2}}+6{{x}^{2}}y- 12x{{y}^{3}}\] |
| B. | \[{{\operatorname{x}}^{3}} 8{{y}^{3}}-6{{x}^{2}}y + 12x{{y}^{2}}\] |
| C. | \[{{\operatorname{x}}^{2}}+ 87y + 7xy - 7xy\] |
| D. | \[7x{{y}^{3}}- 6x - 74{{x}^{2}}y + 2xy\] |
| E. | None of these |
| Answer» C. \[{{\operatorname{x}}^{2}}+ 87y + 7xy - 7xy\] | |
| 40. |
Find the value of (3a + 5b)3 |
| A. | \[27{{a}^{3}}+ 125{{b}^{3}}+ 135{{a}^{2}}b + 2225a{{b}^{2}}\] |
| B. | \[27{{a}^{3}} 125{{b}^{3}} 135{{a}^{2}}b + 2225a{{b}^{2}}\] |
| C. | \[27{{a}^{2}}+ 155{{b}^{2}} 135{{a}^{2}}b - 225{{a}^{2}}b\] |
| D. | \[29{{a}^{2}} 156{{b}^{2}} 156{{a}^{2}}b -225{{a}^{4}}c\] |
| E. | None of these |
| Answer» B. \[27{{a}^{3}} 125{{b}^{3}} 135{{a}^{2}}b + 2225a{{b}^{2}}\] | |
| 41. |
Compounded ratio of (x + y):(x - y), \[\left( {{\mathbf{x}}^{\mathbf{2}}}+\text{ }{{\mathbf{y}}^{\mathbf{2}}} \right)\text{ }:\text{ }{{\left( \mathbf{x}+\text{ }\mathbf{y} \right)}^{\mathbf{2}}}\mathbf{and}\text{ }\left( {{\mathbf{x}}^{\mathbf{2}}}-\text{ }{{\mathbf{y}}^{\mathbf{2}}} \right)\text{ }:\text{ }\left( {{\mathbf{x}}^{\mathbf{4}}}-\text{ }{{\mathbf{y}}^{\mathbf{4}}} \right)\]is: |
| A. | (x + y) : 1 |
| B. | (x - y) : (x + y) |
| C. | \[(1 : \left( {{x}^{2}}- {{y}^{2}} \right)\] |
| D. | \[\left( {{x}^{2}}+ {{y}^{2}} \right) : \left( {{x}^{2}}- {{y}^{2}} \right)\] |
| E. | None of these |
| Answer» D. \[\left( {{x}^{2}}+ {{y}^{2}} \right) : \left( {{x}^{2}}- {{y}^{2}} \right)\] | |
| 42. |
The ratio of the volume of three buckets is 3 : 4 : 5. Buckets contains the mixture of water and alcohol. If the mixture contains water and alcohol in the ratio 1 : 4, 1: 3 and 2 : 5, respectively then find the ratio of water and alcohol when the mixture in all containers are poured in fourth container. |
| A. | 1.4979166666667 |
| B. | 53:157 |
| C. | 6.5784722222222 |
| D. | 35 : 157 |
| E. | None of these |
| Answer» E. None of these | |
| 43. |
Which one of the following is the equation for the statement given below? "Square of a number (x) added to 13 given 44" |
| A. | \[{{x}^{2}}+44=13\] |
| B. | \[13+{{x}^{2}}=44\] |
| C. | \[{{x}^{2}}44=13\] |
| D. | \[13{{x}^{2}}=44\] |
| E. | None of these |
| Answer» C. \[{{x}^{2}}44=13\] | |
| 44. |
The equations \[3x-5y+2=0\] and \[6x+4=10y\] have |
| A. | No solution(s) |
| B. | A single solution |
| C. | Two solutions |
| D. | An infinite number of solutions |
| Answer» E. | |
| 45. |
If one root of the equation \[3{{x}^{2}}-9x=kx-k\] is 2,then the value of k is |
| A. | 4 |
| B. | 3 |
| C. | -6 |
| D. | -8 |
| Answer» D. -8 | |
| 46. |
DIRECTIONS: The questions in this segment consists of two statements, one labelled as ?Assertion A? and the other labelled as ?Reason R?. You are to examine these two statements carefully and decide if the Assertion A and Reason R are individually true and if so, whether the reason is a correct explanation of the assertion. Select your answers to these items using codes given below. Assertion A: 5 is added to both sides of the equation \[x+a=b\] but the value of the equation doesn't change. Reason R: If we perform the same mathematical operation on both sides of the equation its value doesn't change. |
| A. | If both Assertion and Reason are correct and Reason is the correct explanation of Assertion. |
| B. | If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion. |
| C. | If Assertion is correct but Reason is incorrect. |
| D. | If Assertion is incorrect but Reason is correct. |
| Answer» B. If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion. | |
| 47. |
If \[A=\{x:{{x}^{2}}-3x+2=0\}\]and \[B=\{x:{{x}^{2}}+4x-5=0\}\] then the value of A - B is |
| A. | \[\{1,2\}\] |
| B. | {2} |
| C. | \[\{1\}\] |
| D. | {5, 2} |
| Answer» C. \[\{1\}\] | |
| 48. |
Consider the statements given below. (i) If we fail to do the same mathematical operation on both sides of an equality, the equality does not hold. (ii) The value of the variable for which the equation is satisfied is called the solution of the equation. (iii) When we add two algebraic expressions, the unlike terms are added (iv) All monomials, binomials, trinomials and polynomials are called by the name algebraic expressions. Which of the above statements is/are incorrect? |
| A. | only (i) |
| B. | only (ii) |
| C. | only (iii) |
| D. | only (iv) |
| Answer» D. only (iv) | |
| 49. |
Amulya is x years of age now. 5 years ago her age was |
| A. | \[(5-x)\] years |
| B. | \[(5+x)\] years |
| C. | \[(x-5)\] years |
| D. | \[(5\div x)\] years |
| Answer» D. \[(5\div x)\] years | |
| 50. |
The coefficient of \[{{x}^{2}}{{y}^{6}}\] in the term \[-{{x}^{2}}{{y}^{6}}\] is? |
| A. | 0 |
| B. | -1 |
| C. | 1 |
| D. | 6 |
| Answer» C. 1 | |